Consider the entire 2D plane to be an infinite sheet of paper. A circle $C$ having equation $x^2+y^2=9$ is drawn on it. Now several points on the circumference of C are made to be coincident with the fixed point $P(-1,2)$ by folding the paper along different straight lines. All possible crease formed touch a fixed conic having eccentricity $e_1.$  Now another point $Q(-4,2)$  is made to be coincident with several points on circumference of $C$ by folding the paper along different straight lines. All possible such crease formed touch another fixed conic with eccentricity $e_2.$  Finally the paper is folded along different straight lines so that point $Q$  lies on several points on $x$  axis. All possible such crease formed touch another fixed conic with eccentricity $e_3.$  Find the value of $2e_1^2+4e_2^2-6e_3^2=?$